Periodic motions and chaos in power system including power disturbance
School of Aeronautics and Astronautics, Shanghai Jiao Tong University, Shanghai 200240, P.R. China
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Received in final form: 22 January 2019
Published online: 25 September 2019
Single-machine infinite-bus power system is a nonlinear dynamic system with state variable in the sinusoidal function. With traditional analytical approaches, it is difficult to analyze such a nonlinear system since the rotor angle difference cannot always stay in an infinitesimal small value. In this paper, a single-machine infinite-bus power system with power disturbance will be discussed. The implicit discrete maps approach will be applied to solve the periodic motions for such a power system, and the stability condition will be discussed. The analytical expressions for periodic motions for such a single-machine infinite-bus power system can be recovered with a series of Fourier functions. The bifurcation diagram for such a system will be given to show the complexity of the motions when the frequency of the disturbance varies, and 2-D parameter map for chaotic motion will be obtained by calculating the Kolmogorov-Sinai entropy density. From analytical bifurcation for period-1 and period-2 motions, the evolution process of the periodic motion to chaos can be analytically explained.
© EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature, 2019